The Detection of Earnings Manipulation: The Three Phase Cutting Plane
Algorithm using Mathematical Programming
Burcu Dikmena∗
Güray Küçükkocaoğlub
ABSTRACT
The primary goal of this study is to propose an algorithm using mathematical programming to
detect earnings management practices1. In order to evaluate the ability of this proposed
algorithm, the traditional statistical models are used as a benchmark vis-a-vis with their timeseries counterparts. As emerging techniques in the area of mathematical programming yields
better results, application of suitable models expected to result in highly performed forecasts.
The motivation behind this paper is to develop an algorithm which will give a successful
achievement on detecting companies which appeal to financial manipulation. The
methodology is based on cutting plane formulation using mathematical programming. A
sample of 126 Turkish manufacturing firms described over ten financial ratios and indexes are
used for detecting factors associated with false financial statements. The results indicate that
the proposed three phase cutting plane algorithm outperforms the traditional statistical
techniques which are widely used for false financial statement detections. Furthermore, the
results indicate that the investigation of financial information can be helpful towards the
identification of false financial statements and highlight the importance of financial
ratios/indexes such as Days’ Sales in Receivables Index (DSRI), Gross Margin Index (GMI),
Working Capital Accruals to Total Assets (TATA), Days to Inventory Index (DINV).
Key words: mathematical programming, mathematical model, cutting plane algorithm,
earnings management, false financial statements
1. Introduction
Detection of manipulated financial statements by using normal audit procedures becomes an
incredibly difficult task (Porter and Cameron, 1987; Coderre, 1999). First of all, there is a
shortage of knowledge concerning the extensions and characteristics of management fraud.
Secondly, auditors lack the experience necessary to detect manipulated financial statements.
Finally, managers are deliberately trying to deceive the auditors by using new techniques
(Fanning and Cogger, 1998). On the other hand, the nature of accrual accounting gives
managers a great deal of discretion in determining the actual earnings a firm reports in any
a∗
The Scientific and Technological Research Council of Turkey - Space Technologies Research Institute, Ankara, Turkey,
Tel : +90 312 210 13 10/1559, Fax : +90 312 210 13 15, e-mail : burcu.dikmen@uzay.tubitak.gov.tr
b
Baskent University, Faculty of Economics and Administrative Sciences, Ankara, Turkey, Tel : +90 312 234 10 10/1728,
Fax : +90 312 234 10 43, e-mail : gurayk@baskent.edu.tr
1
The terms “earnings management”, “earnings manipulation”, “fraud”, “falsified financial statements” are all
used interchangeably to describe the act of intentional misrepresentation of a firm’s financial statement by
managers.
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given period. Management has considerable control over the timing of actual expense items
(e.g., advertising expenses or outlays for research and development). They can also, to some
extent, alter the timing of recognition of revenues and expenses by, for example, advancing
recognition of sales revenue through credit sales, or delaying recognition of losses by waiting
to establish loss reserves (Teoh et al., 1998). For such managers, who are aware of the
limitations of an audit, standard auditing procedures become insufficient. These limitations
suggest the need for additional analytical procedures for the effective detection of earnings
management practices (Spathis, 2002).
Earnings management literature developed after 80’s has focused increased attention on the
interpretations of accrual accounting practices. In particular, almost all existing empirical
research conducted after Healy (1985) and DeAngelo (1986) have focused on specific
accruals, and Jones (1991), Dechow, Sloan and Sweeney (1995) have focused on all accruals
as being more prone to be used for earnings management purposes.
Later on, Beneish (1997), (1999) adopted a weighted exogenous sample maximum likelihood
(WESML) probit model for detecting manipulation. The model’s variables are designed to
capture either the financial statement distortions that can result from manipulation or
preconditions that might prompt companies to engage in such activity. Beneish (1999)
provides evidence that accrual models have poor detective performance even among firms
whose behavior is extreme enough to warrant the attention of regulators. Where he has stated
that
“Research that uses accrual models to investigate whether earnings are
managed is a growing industry but its foundations are in need of redefinition.”
With the emergence of artificial neural network applications on detecting the underlying
functional relationships within a set of data and perform such tasks as pattern recognition,
classification, evaluation, modeling, prediction and control, several algorithms are developed
to assess the risk of fraud and irregularities in financial statements (Lawrance and Androlia,
1992).
The motivation behind this paper is to develop an algorithm which will give a successful
achievement on detecting companies which appeal to financial manipulation and intend to
estimate the amount of earnings management practices from the publicly available
information. The algorithm overcomes some of the major drawbacks of the existing statistical
techniques and permits to test directly for the presence of earnings management in a sample of
publicly traded 126 Turkish manufacturing firms.
The remaining part of this paper is organized in five sections. In the next section, we provide
a comparison of the theoretical and empirical research conducted on estimating earnings
management practices and describe the existing techniques. Thus, section three discusses the
existing mathematical programming techniques in detection of earnings management
practices with their main assumptions and drawbacks. The following section derives
theoretically the generalized form of the three phase cutting plane algorithm accompanied by
a discussion of its advantages over the most popular existing models as well as of its weak
sides. The results of the application of the algorithm can be found in the last part of section 4.
Section five concludes.
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2. Theoretical background
This section, summarizes the several techniques available for the detection of earnings
manipulation, is composed of three subsections. The first subsection discusses the competing
discretionary accruals models in the earnings management literature developed by DeAngelo
(1986), Healy (1985), Jones (1991), the second subsection discusses the statistical techniques
applied by Hansen et. al. (1996), Beneish (1997, 1999) and Spathis (2002) and the third
subsection reviews the literature on artificial neural network applications to earnings
management practices. A detailed review of our proposed three phase cutting plane algorithm
for the detection of earnings manipulation is provided in sections three and four.
2.1. Discretionary-accruals models
The literature on earnings management has mainly discussed manipulations that are
interpretations of standards, for instance decisions on the level of accruals and most of the
reseach has found that discretionary accrual models can be effective tool for detecting
earnings manipulation as they can expose the unusual figures associated with the reported and
the expected amounts. Prior studies conducted by DeAngelo (1986), Healy (1985), Jones
(1991) on earnings management have concentrated on how accounts are manipulated through
accruals. Accruals management refers to changing estimates such as useful lives, the
probability of recovering debtors and other year end accruals to try to alter reported earnings
in the direction of a desired target (Ayres, 1994). Where The DeAngelo (1986) model uses
last period’s total accruals scaled by lagged total assets as the measure of nondiscretionary
accruals. Healy (1985) uses the mean of total accruals scaled by lagged total assets from the
estimation period as the measure of nondiscretionary accruals. Jones (1991) attempts to
control for the effects of changes in a firm’s economic circumstances on nondiscretionary
accruals.
2.2. Statistical Techniques
The absence of specific professional guidance and a lack of experience with management
fraud have led practitioners and researchers to develop models or decision aids for predicting
management fraud (Hansen et al., 1996)
Using the same data set as Bell et.al. (1993), Hansen et al., (1996) used a powerful
generalized qualitative-response model, EGB2, to model and predict management fraud based
on a set of data developed by an international public accounting firm. The EGB2 specification
includes the probit and logit models and incorporates the asymmetric costs of type I and type
II errors. The results demonstrate good predictive capability with an overall accuracy of 85.3
percent.
In the same area, Beneish (1997), (1999) used a weighted exogenous sample maximum
likelihood (WESML) probit model for detecting manipulation. The model’s variables are
designed to capture either the financial statement distortions that can result from manipulation
or preconditions that might prompt companies to engage in such activity. Beneish (1997),
provides evidence that accrual models have poor detective performance even among firms
whose behavior is extreme enough to warrant the attention of regulators.
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2.3. Neural Network Models
Artificial Neural Network technology is a knowledge induction technique that builds a
classification model by finding any exisiting patterns of input data. Neural Networks, consists
of a set of interconnected processing nodes, arranged in input, hidden and output layers. Data
flows through this network in one direction, from the input layer to the output layer. Data first
enters the network through nodes in the input layer. While the input nodes pass data to the
nodes in the hidden layer(s) to enable the network to model complex functions. The nodes in
the output layer both receive and process all inputs (Coakley and Brown 2000).
A number of studies conducted by Green and Choi (1997), Fanning and Cogger (1998), Lin
et.al. (2003) have shown the power of neural network applications on the detection of
fraudulent financial statements.
Green and Choi (1997) presented the development of a neural network fraud classification
model employing endogenous financial data and find that their model performs well at this
classification. Fanning and Cogger (1998) use an artificial neural network to develop a model
for detecting management fraud. Using publicly available predictors of fraudulent financial
statements, they find a model of eight variables with a high probability of detection. Lin et.al.
(2003) created a fuzzy neural network to investigate the utility of information technologies
such as an integrated system of neural network and fuzzy logic for fraud detection.
3. Literature review on the existing mathematical programming techniques
3.1. Mathematical programming in discriminant analysis
As mentioned above statistical techniques are widely used in the area of earnings
manipulation. However, as emerging techniques such as mathematical programming yields
better results as in the area of macroeconomical forecasting (Reagle and Salvatore, 2000),
bankruptcy prediction (Freed and Glover, 1981), sectoral and political policy examinations
(Bauer and Kasnakoglu, 1990), economic trend forecasting (Tingyan, 1990), insurance policy
and profit calculations (Waters, 1990), application of a suitable model is expected to result in
highly performed forecasts in the area of earnings management practices. Mathematical
modeling techniques in earnings management practices are put into agenda with the study of
Spathis et.al. (2002), where financial data of 76 firms, half of which is known to resort
manipulation, is taken into consideration to develop a forecasting tool by UTADIS
methodology. Although this study shows a superficial performance; using just one year data
and distribution of the sample data (50% manipulated - 50 % non-manipulated) make the
model to be questionable. In order to be used in real life problems, models should not be year
specific. Although this (time) dependence on annual economic conditions can be eliminated
using ratios instead of raw information, it is expected that multiple year data is the most
reliable input when forming a model. Another point that needs to be discussed is the
distribution of manipulated and non-manipulated firms, for the sake of realibility of
discrimantion studies; it is not advised to use the same number of observations from different
groups (Luoma and Laitinen, 1991).
In this regard, our study compromises of a larger sample size with different sample
distribution where the proposed algorithm is run on a data of eleven years. In order to
decrease time dependency and form a more general and reliable model, financial reporting of
manufacturing companies listed on the Istanbul Stock Exchange (ISE) between the years 1992
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and 2002 is used. The sample size (number of firms) is 126 firms (including 21 manipulated
and 105 non-manipulated firm data) and the model is formed on the basis year of 1997.
3.2. Mathematical Modelling in Discriminant Analysis - Definition
The use of mathematical modeling in discriminant studies began with Freed and Glover
(1981). In pursuit of this study, mathematical models on different areas of discrimination have
been successfully conducted. These models consider several criterias with different
constraints and try to obtain high performance on prediction of group membership.
Considering a general classification problem, the steps of discrimination can be defined as:
Step I. Detecting the group of sample observations (i.e: manipulated vs. non-manipulated),
Step II. Determination of discrimination criterias (variables) (i.e: ratios) and gathering
related data of observations,
Step III. Determination of discriminant scores (combination of predefined variable data)
and cut off point (which is thougt to be effective on class determination),
Step IV. Application of the model on new observations, classifying them.
In step III, a score (discriminant score) is obtained by calculating the weighted sum of the
variables determined and using the data collected in step II. This score would determine the
observation’s class. Another point is to determine the cut off point which is a benchmark for
the observations discriminant score to determine their original class. The observation with a
score above this value (cut off point) will be assigned to one class and the observation with a
score below the cut off point will be assigned to another. The following section details the
description of this procedure by mathematical programming technique.
The observation data gathered and the weights designated to variables’ effect on discriminant
score are named as “xij” and “wi” (i representing the observation and j representing the
variable) respectively. The cut off point which is a benchmark for the observations’
discriminant value is represented by “c”. Observations with a higher value of discriminant
score than the cut off point is a member of one group and with a lower value is a member of
the other. The main aim of this kind of model is to weight the set of variables which
maximizes the distance between the observations’ discriminant score and the cut off point.
The sembolic representation of this model is shown below (Freed and Glover, 1981a):
w1 x1 j + w2 x2 j ≥ c designated to one group
w1 x1 j + w2 x2 j ≤ c designated to other group
When inserting the variable d, which shows the distance between the observations’
discriminant score and the cut off point, to the model the equation becomes:
w1 x1 j + w2 x2 j − d ≥ c designated to one group
w1 x1 j + w2 x2 j + d ≤ c designated to other group
Inserting d to the model, the probability of wrong classification arises. Non-existance of d
results in either 100% success performance (which is not a real case) or no solution case.
With the introduction of objective function of maximizing the distance d the model is defined
as below:
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max d
w1 x1 j + w2 x2 j − d ≥ c ( first group )
w1 x1 j + w2 x2 j + d ≤ c (sec ond group )
no restriction of sign on w1, w2 and d
In such a model, d is a measure of the performance of the model. As d increases the
performance of the model increases. No restriction rule on the sign of d minimizes the group
intersection, in turn, wrong classification. Maximization of d means maximizing the minimum
distance of observations’ discriminant score to cut off value. In some models d may be
observation’s variable. This can be symbolized as:
m
Max ∑ d j
j =1
wi xij + wi xij − d j ≥ c ( first group )
wi xij + wi xij + d j ≤ c (second group )
(no restriction of sign on w1, w2 and dj )
(1)
3.3. Discriminant Analysis by Classical Modelling Methods
There are several models for solving classification problems. In this section, models, which
are widely used in literature, are described with their advantages and disadvantages.
MMD-1 (Freed and Glover, 1981a) aims to minimize the maximum deviation (distance of
observation classification score to cut off point, d). Model can be represented as:
MMD-1 (Freed and Glover, 1981a):
Z = max d
Xiw + d ≤ c
Xiw - d ≥ c
c: cut-off point, constant for each observation, no restriction in sign
d: deviation, constant for each observation, no restriction in sign
w: coefficient matrix, no restriction in sign
A characteristic of MMD-1 is that, unbounded solution means a perfect classification.
However, this model may yield trivial solution as well. In order to avoid trivial solution,
matrix transformation may be applied. But this time optimal solution can fade away with the
elimination of the trivial solution. Therefore, it can be said that matrix transformation is not
applicable for this kind of model.
Another model, named as MMD-2 (Freed and Glover, 1981b) investigates e, which is
deviation of wrong classified observation (can also be called as external deviation), rather
than d. Model, tries to minimize the wrong classification deviation and “c” is again a constant
for all observations.
MMD-2 (Freed and Glover, 1981b):
z = min e
Xiw - e ≤ c
Xiw + e ≥ c
c: cut-off point, constant for each observation, no restriction in sign
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e: external deviation of wrong classified observation, positive
w: coefficient matrix, no restriction in sign
The solutions of MMD-2 are always bounded, but trivial solution can not be avoided. Matrix
transformation is not applicable for this kind of model as well. In order to avoid trivial
solution normalization constraint, which is w’+ c = s, “s” as a positive constant, can be used
(Freed and Glover, 1986a). This constant can also eliminate the optimal solution. Therefore
p
one other normalization constraint,
∑
i =1
w + c ≤ s and
p
∑w+ c =s
may be another
i =1
alternative for preventing the elimination of optimal solution (Freed and Glover, 1986b).
Another normalisation constraint is generated by Erenguc and Koehler (1990) which is
formulized as w’= s. However, this constraint may limit the feasible region.
Another model suggested by Hand (1981) also minimizes the external deviation:
min (e1′+ e2′)
Xiw – e1 + c ≤ -bi
Xiw + e2 + c ≥ bi
c: cut-off point, constant for each observation, no restriction in sign
e1, e2: external deviation, positive
w: coefficient matrix, no restriction in sign
b1 and b2: positive matrix, generally determined to be equal
This model generates less trivial solution; therefore this can be said to be more stable.
However strict classification may form a gap between the groups. Avoiding use of “b” values
may remove the gap. For trivial solution, the constraint w’1+ c = s can be used (Koehler,
1989).
Some models (Freed and Glover, 1981a,b; 1986a,b) consider internal (deviation of right
classified observations, i) and external deviations seperately. Therefore, four types of
objective function can be summarized as:
Objective 1: minimizing maximum external deviations (MSID-1)
Objective 2: maximizing minimum internal deviations (MSID-2)
Objective 3: maximizing weighted average of internal deviations of group 1 and group 2
(MSID-3)
Objective 4: minimizing weighted average of external deviations of group 1 and group 2
(MSID-4,5)
MSID-6 (Bajgier and Hill, 1982) model depends on the idea of maximizing the internal
deviation while minimizing the external deviation. The model is:
min H1(e1+e2)- H2(i1+i2)
X1w - i1+ e1-c=0
X2w - i2 + e2-c=0
i1, i2, e1, e2 ≥ 0
H1, H2: weight of internal and external deviations, positive
c: cut-off point, constant for each observation, positive
e1, e2: external deviation, positive
i1, i2: internal deviation, positive
w: coefficient matrix, no restriction in sign
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It is rare to obtain a trivial solution for this model. The only case when no solution exists is
where H1<H2 condition is satisfied (Koehler, 1989). H1 and H2 should be carefully determined
in order not to get the no solution case.
There are also hybrid models which merge one or more of the objectives mentioned above.
Since these combined forms of models are very detailed for the scope of this paper, they are
excluded. However, further readings about these studies can be found in (Glover et. al.,1988;
Glover, 1988).
Another model suggested by Retzlaff-Roberts (1996) considers the ratio of internal deviation
to external deviation. This model combines the advantages of several other models described
above. The ratio obtained will be unitless and this will yield a more reliable solution. This is
also a hybrid model whose objective function is defined in a different way. The objective
function of model is defined as:
max
k0i0 + ∑ ki ii
i∈G
h0 e0 + ∑ hi ei
i∈G
k, h: weight coefficients
In order to linearize the model, the denominator is equalized to unity and the objective
function is formulated to maximize the numerator.
The model can be expressed as:
max h0α 0 + ∑ hiα i
i∈G
s.t
k 0 β 0 + ∑ ki β i = 1
i∈G
X 1w − α 0 − α i + β 0 + β i = c, i ∈ G1,
X 1w + α 0 + α i − β 0 − β i = c, i ∈ G2,
α 0 , α i , β 0 , βi ≥ 0
w: coefficient matrix, no restriction in sign
Another group of programming models used in classification is mixed integer programming
models. The first model discussed here is suggested by Bajgier and Hill (1982). Model
minimizes external deviation plus number of wrong classified observations and maximizes the
internal deviation. Model can be demonstrated as follows:
min P1 (I1+I2)+ P2 (e1+e2)- P3 (i1+i2)
Xiw + i1- e1-c=0
Xiw – i2 + e2-c=0
e1≤M I1
e2≤M I2
i1, i2, e1, e2 ≥ 0
I1, I2: binary variables
M: big number
P1, P2, P3: positive weights
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MIP-2 considers just one objective which is minimizing the number of wrong classified
observations. Deviation is not considered in this model.
MIP-2 (Freed and Glover, 1986b; Glover, 1988; Stam and Joachimstahler, 1988):
min I1+ I2
X1w≤ c+ M I1
X2w≥ c- M I2
Since there is no sign restriction for the cut-off value c in this model, it is possible to come up
with a trivial solution such as c=0, w=0, I1=0, I2=0. In the case c is positive, w=0, I1=0,
I2=(c/M)1 and the objective function being equal to (cN2/M) is also the solution to the
problem. If M is big enough (cN2/M) will merge to zero which will yield a trivial solution.
Another mixed integer programming technique determines an an upper level/lover level
boundary around the cut-off value and observations placed in this area is examined. The
model can be shown as:
MIP-3 (Gehrlein,1986)
min I1+I2
X1w≤(u1-c)+ M I1
X1w≥(l1-c)- M I1
X2w≤(u2-c)+ MI2
X2w≥(l1-c)- M I2
u1- l1≥ ε
u2- l2≥ ε
l1- u2+Ml12≥ ε
l2- u1+Ml21≥ ε
I12+ I21 = 1
w, u1, u2, c, l1, l2 :no restriction in sign
I12, I21: binary variables
M: big number
ε: small number
MIP-4 (Erenguc and Koehler, 1988), which is very similar to MIP-2, which is only different
by the normalization constraint w≠0. This constraint makes all the possible solutions to take
place in the solution set. In addition to that, if that constraint does not work, Xiw ≤ c+MI1
constraint can be replaced by X1w ≤ c1+ε (Erenguc and Koehler, 1988).
3.4. Mathematical Modelling versus Statistical Techniques
Statistical techniques depend on basic assumptions. They can be listed as:
1. groups are seperate and defined properly
2. samples are selected from the population randomly
3. variables distribute normally
4. equal variance-covariance matrix.
There are many studies in literature comparing the performance of mathematical modelling
and statistical techniques. Depending on these studies, some conclusions can be remarked.
They can be summarized as follows:
1. Mathematical modelling is superior over statistical techniques, when observations
distribution is not normal. Financial data is generally not normal, in fact bent right
(Deakin, 1976). Therefore mathematical modelling is a better tool for financial
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2.
3.
4.
5.
6.
forecasting (Bajgier and Hill, 1982; Freed and Glover 1986a; Joachimstaler and Stam,
1988; Lam and Moy, 1997).
Statistical techniques have better performance for normal distibution and equal
variance-covariance conditions. This is also basic assumption in statistical models.
Bajgier and Hill (1982),
Mathematical modelling techniques have higher forecasting performance when groups
highly intersect. One of the main assumptions for statistical techniques is that groups
should have different average vectors (Hosseini and Armacost, 1994).
Mathematical modelling techniques are more suitable tools when individual weights
appointed to observations are needed (Erenguc and Koehler, 1990; Lam and Moy,
1997).
Statistical techniques are more sensitive to outliers than mathematical techniques
(Glorfeld and Olson, 1982).
When the number of observations of the groups are not balanced, mathematical
modelling have superior results than statistical techniques (Markowski, 1994).
All these remarks show that, the performance of the mathematical modelling will be superior
to the statistical technique when financial data is used for prediction.
MCDM procedure begins with decision maker’s formation of an alternative set, A = (a1, a2,
a3,… ak) (companies). In the second stage, these alternatives are analised considering several
criterias [g = (g1, g2, g3,.. gn)] (financial ratios, operational ratios etc.) in order to obtain
optimum solution. The optimum solution stands for a solution which is satisfactory and not
overcomed by any other solution. Examining the general logic of the model, it can be seen
that this is a pairwise comparison of alternatives, such as:
If gji > gki , aj > ak
aj alternative is favored to ak
If gji = gki ,
a j ~ ak
aj alternative is indifferent to ak
There are some different MCDM models which chose the best alternative, which classify the
groups or rank the alternatives according to their performances.
Some MCDM techniques used in financial area are: (Zopounidis, Doumpos, 2002):
1. Analytic Hierarchy Process - AHP (Srinivasan and Ruparel, 1990)
2. Outranking relations: ELECTRE (Bergeron et.al., 1996; Andenmatten, 1995)
3. Preferential Classification: UTA, UTADIS, MHDIS (Zopounidis, 1995; Zopounidis and
Doumpos, 1999; Doumpos and Zopounidis, 1999; Doumpos et.al., 2002)
4. Rough Set Theory (Slowinski and Zopounidis, 1995).
Mathematical programming techniques are new in the field of manipulation forecasting.
Doumpos and Zopounidis (2002) who worked on mathematical programming previously
applied UTADIS method in order to obtain a high performance of financial manipulation
forecasting. UTADIS being mainly a Multi Criteria Decision Making (MCDM) method, aims
to classify the observations into different groups.
General form of MCDM is given as:
Max./Min. [g1(x), g2(x), g3(x),… gn(x))]
s.t. x є B
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where x stands for variable set vector, g objective function and B optimal solution. In fact, it is
not so easy, even not probable, to optimize all the objective functions. Therefore, it is aimed
to get a compromise solution of all, where this solution can not be defeated by other solutions.
In a more detailed way by UTADIS (UTilities Additives DIScriminantes; Jacquet-Lagreze,
1995; Doumpos and Zopounidis, 1997, 2002), decision maker determines the alternatives
without prioritizing them. Instead, groups formed by these alternatives are classified (C1> C2>
C3>… Cq). Model can only solve this classification problem if the conditions given below are
provided:
m
U ( g ) = ∑ u i ( g i ) ∈ [0,1]
i =1
s.t
U(aj) ≥ t1
t1 > U(aj) ≥ t1
∀ aj є C1
∀ aj є C2
………..
………..
U(aj) < tq-1
∀ aj є Cq
t: upper and lover bound
4. Aim of the Study
The primary goal of this study is to introduce a new algorithm for mathematical programming
to detect earnings management practices and expects to yield higher level of performance than
other techniques used in this area. Besides, the performance of the developed algorithm is
compared with a statistical technique and the relative efficiency of mathematical modelling
and statistical technique is discussed. In this regard, financial data of the 126 ISE firms is
applied to a statistical model and a mathematical model in order to compare the performances.
4.1. Data
Financial statement data are obtained from the database maintained by the Istanbul Stock
Exchange. The sample consists of 126 Turkish manufacturing companies listed during the
period from 1992 through 20022. Manipulators were identified from Istanbul Stock Exchange
(ISE)’s and Capital Markets Board of Turkey (CMBT)’s weekly bulletins issued from 1992
through 2002, where these companies had to restate their earnings to comply with the
CMBT’s accounting standards at the request of the Board’s internal investigation. Capital
Markets Board of Turkey (CMBT), investigated these 126 companies’ financial statements
corresponding to the years 1992-2002, and detected earnings management practices in 168
observations and no signs of earnings management practices in 1.040 observations. To find
out these investigations conducted by CMBT, where manipulation of financial information
existed and the cases where manipulation of financial information did not exist, ISE’s daily
bulletins corresponding the dates between 01.01.1992-31.07.2004 and CMBT’s weekly
bulletins corresponding to the dates between 01.01.1996-31.07.2004 were investigated using
some key words (financial statements, balance sheet, income statement, profit, loss, income,
2
In accordance with the International Accounting Standard No. 29 “Financial Reporting in Hyperinflationary
Economies” ("IAS 29"), ISE listed companies adjusted their financial statements for inflation effects in 2003,
due to this fact, we have only included years 1992 through 2002 for sound comparison.
11/28
cost, audit report, capitalization, and restatement). According to the information gathered
from these bulletins, the companies which were determined and announced to the public as
having exercised manipulation of financial information as a result of the CMBT’s
investigations and/or the ones which received qualified audit opinion changing the values in
their financial statements about their publicly available financial statements or the companies
which had changed the values in their financial statements after balance sheet date were
considered as the companies which exercised manipulation of financial information. In
addition, the companies which had changed the information in their financial statements
prepared to be registered with the CMBT during the investigations done by CMBT were also
considered as the companies which exercised manipulation of financial information.
The model is formed on the basis of year 1997 and applied to all other years’ data in order to
measure the performance of the model. There are 126 firms with eleven years data, each of
which is considered to be an element, therefore resulting in a total of 1260 observations.
However, because of the deficiencies in the data, 27 observations are left out from the
observation set and the study is carried out with 1233 observations. In base year 1997, there is
a total of 126 firms, of which, 21 of them are manipulated their financial statements and had
to restate their financial statements in accordance with the CMBT’s directives. Our research
relies on the assumption that the Capital Markets Board of Turkey has (on average) correctly
identified firms that intentionally overstated reported earnings.
4.2. Methodology
The methodology carried out in this study is given in Figure 1. As seen in the figure,
statistical techniques first determine the manipulators and nonmanipulators then clusters
manipulators as 4 different groups: very significant danger group, serious risk of earnings
group, grey zone group, no evidence group. Mathematical modelling follows a step by step
procedure, determining each group individuals once at a time. The first step is a mixed integer
programming approach which aims to determine the group membership in high performance.
In the consequent stages linear programming approach tries to minimize the distance between
the observations, to make clusters, and to minimize the wrong classified distance.
12/28
Data gathering
(10 financial data of 10 year 126 firms)
PART I: Formulation of the model
with the data of year 1997
Formulation of the model with the
data of year 1997
PART II- STEP I: Classification of
non manipulator candidates and
very significant danger group by
MIP approach
Classification of manipulators and
non manipulators by PROBIT
PART II- STEP II: Determination
of serious risk of earnings group by
LP approach
Clustering of manipulators as being
very significant danger, serious risk
of earnings, grey zone and no
evidence
PART II- STEP III: Determination
of grey zone and no evidence group
by LP approach
Figure 1 – Methodology
4.3. Variable Measurement
To examine the motivations for earnings management firms, we require measures of the
various constructs in the following section. Although there is no formal theoretical guidance
on the selection of variables in the earnings management literature, through a review of
CMBT practices and empirical research, especially on Beneish’s studies (1997, 1999), we
identified 10 financial ratios and indexes
The functions and calculation methods of 10 independent variables that have been determined
for our empirical study are explained below3.
3
The data set and explanations related to 10 independent variables determined for our study are taken from the
studies of Beneish (1997, 1999), Küçüksözen (2005) and Küçüksözen and Küçükkocaoğlu (2005).
13/28
Leverage Index (LVGI)
LVGI =
Total Debt t /Total Assetst
Total Debt t -1 /Total Assetst -1
The LVGI is the ratio of total debt to total assets in year t relative to the corresponding ratio in
year t-1. An LVGI greater that 1 indicates an increase in leverage. This variable was included
to capture incentives in debt covenants for earnings manipulation.
Inventory Index (DINV)
DINV =
Inventories t /Sales t
Inventories t −1 /Sales t −1
The DINV is the ratio of inventories to sales in year t relative to the corresponding ratio in
year t-1. According to Beneish (1997) firms generally use different inventory methods (LIFO,
FIFO, Average Costing) in order to manipulate the profits.
Financial Expenses Index (FEI)
FEI =
Financial Expensest /Salest
Financial Expensest −1 /Salest −1
The FEI is the ratio of financial expenses to sales in year t relative to the corresponding ratio
in year t-1. Most of the financial manipulation cases detected by the CMBT in Turkey
involves in the manipulation of financial expenses where firms allocate these expenses into
their accounts receivables, inventories, next year’s expenses, associates, plant, property and
equipment, intangible assets, and/or continuing investments, instead of recording financing
expenses as current period expenses on the income statement. In this regard, company’s
managers will be able to reach their own final results by capitalizing important portion of
financing expenses by increasing profit. Or, to decrease profit, they will record financing
expenses as current period expense. Due to the flexible structure of tax law on the subject of
recording financing expenses as expense for current period or capitalizing them, the
applications of financial information manipulation are enchained. Within this framework, it is
assumed that there is a correlation between this index and manipulation of financial
information.
Days’ sales in receivables index (DSRI)
DSRI =
Receivablest /Salest
Receivablest −1 /Salest −1
The DSRI index shows the change in receivables at time t by comparing them at time t-1
according to sales. As long as there is no extreme change in the policy of credit sales of the
company, this index is expected to have a linear structure. An important increase in this index
is based not only on the accountancy of consignment sales recorded as trade receivables and
14/28
sales toward the increase in income as well as profit of the company but also on the creation
of trade receivables from current accounts of group companies. These two applications are
considered as the indicators of the manipulation of financial information. According to
Beneish (1997) a large increase in days’sales in receivables could be the result of a change in
credit policy to spur sales in the face of increased competition, but disproportionate increases
in receivables relative to sales could also suggest revenue inflation.
Gross Margin Index (GMI)
GMI =
(Salest −1 − Cost of Goods Sold t −1 )/Salest −1
(Salest − Cost of Goods Sold t )/Salest
The GMI is the ratio of the gross margin in year t-1 to the gross margin in year t. When the
GMI is greater than 1, gross margings have deteriorated. Lev and Thiagarajan (1993)
suggested that deterioration of gross margin is a negative signal about a company’s prospects.
So, if companies with poorer prospects are more likely to engage in earnings manipulation.
We expected a positive relationship between GMI and the probability of earnings
manipulation.
Asset Quality Index (AQI)
Current Assetst + PPEt )
/
Total Assetst
AQI =
Current Assetst -1 + PPEt -1 )
(1 −
/
Total Assetst -1
(1 −
Asset Quality Index shows the change in other non current assets except current assets and
plant, property and equipment within total assets by compared to previous year. If the AQI is
greater than 1, the company has potentially increased its involvement in cost deferral. An
increase in asset realization risk indicates an increased propensity to capitalize, and thus defer,
costs (Beneish,1997). Therefore, we expected a positive correlation between asset quality
index and financial information manipulation.
Sales Growth Index (SGI)
Sales
SGI =
t
Sales
t −1
Sales growth does not necessarily prove the manipulation of financial information. According
to the professionals, growing companies that take sales growth into account are more inclined
to manipulate financial information compared to other companies; because, the structure of
debt/equity and the needs of resources create pressure on managers in order to increase sales
in these companies. If a decrease in the prices of common stock is observed related to slowing
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down on the sales growth of these companies, more pressure will be seen on managers in
order to manipulate financial information in such a case.
Depreciation Index (DEPI)
DEPI =
Depreciationt −1 /(Depreciationt −1 + PP& Et −1 )
Depreciationt /(Depreciationt + PP& Et )
The DEPI is the ratio of the rate of depreciation in year t-1 to the corresponding rate in year t.
A DEPI greater than 1 indicates that the rate at which assets are being depreciated has slowedraising the possibility that the company has revised upward the estimates of assets’ useful
lives or adopted a new method that is income increasing (Beneish, 1997). In this study,
depreciation expenses were not directly calculated by using data from balance sheet and
income statement. For this reason, depreciation expense of any period is determined as the
difference between accumulated depreciation of current period and accumulated depreciation
of previous period. This amount may create difference in terms of current period’s
depreciation expense. In this context, in depreciable assets, the change in current period will
vary the amount of accumulated depreciation without affecting depreciation expense very
much. Also, as it is mentioned below, this approach is going to be more appropriate to
calculate depreciation expense by considering that these companies belong to manufacturing
sector as well as there is no big change in their depreciable assets.
As mentioned above, if this proportion is greater than 1, this situation indicates that the
company decreases its depreciation expenses in order to declare high profit by considering
that the expected useful life of plant, property and equipment will be lengthened or the
method of depreciation will be changed in such a way to reduce expenses. On the other hand,
it is expected that this index will not change very much by considering that companies which
constitute our study are manufacturing companies in reel sector. In manufacturing industry, it
is not expected that depreciable assets of these companies will increase or decrease very much
in the context of purchases and sales. By taking this factor into account, if an important
increase is observed on this index on a yearly basis, this situation is accepted as an indicator
of financial information manipulation. For this reason, it is assumed that there is a positive
correlation between depreciation expenses and financial information manipulation in our
model.
Sales, General and Administrative Expenses Index (SGAI)
(Mkt. Sales Expenses + Gen. Adm. Expenses ) / Gross Sales
SGAI =
t
t
+ Gen. Adm. Expenses
(Mkt. Sales Expenses
t −1
t
) / Gross Sales
t −1
t −1
The SGAI is the ratio of sales, general and administrative expenses to sales in year t relative
to the corresponding measure in year t-1. It is expected that there is a correlation which will
not change for a long time between marketing, sales, distribution and general administrative
expenses to sales. These expenses will change according to main activities of the company; in
other words, these expenses are variable expenses based on change in sales. In this context, it
is expected that sales are manipulated or expenses are under priced in case of important
changes which take place in this variable, in other words, in case of a significant decrease in
16/28
the proportional relationship between sales and these expenses, as long as there is no
important increase in efficiency, it is assumed that there is a positive correlation between
SGAI index and financial information manipulation.
Leverage Index (LVGI)
LVGI =
(LTDt + CurrentLiabilities t ) /TotalAssetst
(LTDt −1 + CurrentLiabilities t −1 ) /TotalAssetst −1
The LVGI is the ratio of total debt to total assets in year t relative to the corresponding ratio in
year t-1. An LVGI greater that 1 indicates an increase in leverage. This variable was included
to capture incentives in debt covenants for earnings manipulation.
Total Accruals to Total Assets Index (TATA)
( TATA ) =
Δ Current Assets − Δ Cash and Marketabl e Securitie s −
(Δ Short Term Debt − Δ Current Portion of the Long Term Debt −
Δ Deferred Taxes and some other Legal Laibilitie s) − Depreciati on Expenses
Total Assets
t
t
can be calculated as above. When we calculate total accruals to total assets index, we try to
show the change in debt-receivables and revenue-expense items within the framework of
accrual basis and based on company’s administrative initiatives. The reason behind this
variable being in this model, is to determine any manipulation of financial information
applications based on increase in revenue or decrease in expense or vice versa within the
framework of accrual basis. In this context, if this variable, in other words, non-cash working
capital increases or decreases dramatically, it is assumed that manipulation of financial
information takes place.
4.4. Mathematical Model Applications
As mentioned above, the algorithm used to determine the manipulators is a three step
procedure consisting of application of three mathematical models after determination of
variables (financial ratios) to be used in models. The first model is a MIP approach, which is
different from other consequent stages, in the fact that it contains some integer variables in the
objective function. Second and third stages are LP approaches. While MIP approach tries to
maximize the number of true classification number and the internal deviation minus external
deviation, LP tries to maximize the internal deviation minus external deviation. The model
can be formulated as:
17/28
STEP I – Mixed Integer Programming (detection of very significant danger group)
∑ [t(bin
m
max
i =1
n
+
i
/(m + n) + d(i)) − q(bin i− /(m + n) + e(i))
]
p
∑∑ nm(k, j) cof(j) + d(k) − e(k) ≤ c − ε
(1)
k =1 j=1
m
p
∑∑ m(i, j) cof(j) − d(i) − e(i) ≥ c + ε
(2)
d(k) M ≥ bin +k
e(k) ≤ M bin −k
(3)
d(i) M ≥ bin i+
e(i) ≤ M bin i−
(4)
i =1 j=1
bin i+ + bin i− ≤ 1
(5)
bin +k + bin −k ≤ 1
m: number of manipulated cases
n: number of nonmanipulated cases
i: manipulated case
k: nonmanipulated case
c: cut off point
j: variable number
p: number of coefficients
t,q: internal and external deviation weights
cof(j): coefficient of jth variable
d(i): internal deviation of manipulated case
e(i): external deviation of manipulated case
d(k): internal deviation of nonmanipulated case
e(k): external deviation of nonmanipulated case
STEP II – Linear Programming (detection of serious risk group)
n
∑ d(k) + e(k)
min
k =1
n
p
∑∑ nm(k, j) cof(j) − d
k =1 j=1
2
(k) + e 2 (k) = c 2
d 2 (k) M ≥ bin +k
e 2 (k) ≤ M bin −k
bin +k + bin −k ≤ 1
18/28
STEP III – Linear Programming (detection of grey zone and no evidence group)
s
∑ d(k) + e(k)
min
k =1
s
p
∑∑ nm(k, j) cof(j) − d
k =1 j=1
2
(k) + e 2 (k) = c 2
d 2 (k) M ≥ bin k+
e 2 (k) ≤ M bin −k
bin +k + bin −k ≤ 1
s: number of grey zone and no evidence groups member
As can be seen from the method explained above, the first step, which classifies the very
significant danger group, tries to maximize, both the number of correctly classified
observations and the amount of internal deviation d minus external deviation e. Maximization
of the difference between the internal and external deviation bring about the maximization of
internal deviation and minimization of external deviation. By using weights (t and q), model
can prioritize the correct classification and decreases wrong classified observations. These are
type I and type II indicators. Increasing t (weight of correct classified observation and internal
deviation), results in a decrease in type I error; whereas increasing q results in a decrease in
type II error. This, in turn, can give the decision maker the chance of formulation of the model
according to the problem’s priority. Since the aim of this study is determine the firms which
are manipulators, type I error is more important for this model. Therefore, t is determined to
be 3 whereas q is 1 for this calculation. Also using ε (a very small number), avoids the
placement of observations on the cut-off point which, in fact, is a typical problem very often
encountered in classification problems. cof (j) is a free variable which means that there is no
sign restriction for the coefficient of variables, since some variables may effect the objective
value positively while some others effect in the negative way. For some models, restriction of
coefficient can be useful in order to avoid unbounded coefficients which yields unbounded
p
objective values by adding the constraint ∑ cof(j) = 1 . In this study the model is formulated
j=1
by using this constraint as well however results have shown that addition of restriction of
coefficients decreases the efficiency of the model.
Step II minimizes both type of deviations to make the observations form clusters composed
observations which are at optimal adjacency. Also the constraint bink+ + bink− ≤ 1 is added to
the problem in order to restrict the model in cases of both internal and external deviations are
grater than zero. As the result of step II, the second cut off point (c1) divides the serious risk
of earnings zone from others. Like the second step, step III results in the third cut off point
(c2) which determines the grey zone as well as the no evidence zone.
The graphical representation of step I, step II and step III procedures are given in Figure 2 and
Figure 3 respectively. As shown in Figure 2 only the observations determined to be
manipulators are obtained in classification. Similarly, observations determined to be either in
the serious risk of earnings zone, grey zone group or in no evidence group (zone) is applied in
the model so that these observations are placed in the right groups (Fig.3).
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Figure 2. Classification of Very Significant Danger Cases (Step I)
Figure 3. Determination of Very Serious Risk, Grey and No Evidence Zone (Step II &III)
4.5. Application of Model
As indicated before, the first part of the study forms a model by using 1997 data. In the
second step, the formulation deduced, is applied to the years 1992 through 2002 in order to
evaluate the performance of the model. The first and the second steps are both linear models.
The weights of the variables in Step I are listed in Table 1.
20/28
Table 1 – Coefficients (weights) of independent variables (financial ratios/indexes) in Step I
Independent Variable (Financial Ratios)
Days’ Sales in Receivables Index (DSRI)
Gross Margin Index (GMI)
Total Accruals to Total Assets (TATA)
Days to Inventory Index (DINV)
Leverage Index (LVGI)
Depreciation Index (DEPI)
Sales, General and Administrative Expenses Index (SGAI)
Sales Growth Index (SGI)
Asset Quality Index (AQI)
Financial Expenses Index (FEI)
STEP I
Coefficients
16,4952
-13,1584
8,3547
8,1473
-2,5999
1,8112
1,6927
-1,559
1,2698
0,6528
As seen in in Table 1, Gross Margin Index, Sales Growth Index, Leverage Index are inversely
proportional to the score of the observation. This means that the smaller the firms’s gross
margin index, the greater the probability of manipulation. This claim is also true for Sales
Growth and Leverage Indexes as well.
Another invention deduced fom the model is that the first variable, which is days' sales index,
is the most effective variable to the result of the firm’s status, whether it’s a manipulator or
nonmanipulator. The second highly weighted variable is Gross Margin Index with a
coefficient of -13,1584 (also remember that this is an inversely proportional variable to the
discrimination score of the firm). Least effective variable with a coefficient of 0,6528 is
financial expenses. As mentioned above, most of the financial manipulation cases detected by
the CMBT in Turkey involves in the manipulation of financial expenses, for this reason, we
have added this variable into the model. However, the model shows that this is not an
important for the discrimination; therefore the weight of the ratio is appointed to be minimal.
The model’s cut-off value is found to be 15,7112. The firms with a higher score is said to be
manipulators (very significant danger group). There is also a probabilistic chance of being
manipulator for the firms below this point. In order to group these firms, another model
should be applied. The aim of the second step is to classify the remaining observations. As the
second and third step solutions obtained, serious risk of earnings, grey zone and no evidence
groups are clarified. The results obtained by application of all three steps are given in Table 2.
Since the aim of the study is to determine whether the firm is a manipulator or not, type II
error is underestimated and classification performance is calculated mainly according to
whether the model determines a manipulator firms to be a manipulator or not.
21/28
Table 2 – Classification of the firms as the result of the analysis
Year
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
Total
Number of firms determined as
manipulators at the end of the
analysis
13
18
15
19
21
20
15
16
23
11
139
Number of actual
manipulators
Performance (%)
12
12
11
18
21
16
12
12
17
8
171
92,3
66,7
73,3
94,7
100,0
80,0
80,0
75,0
73,9
72,7
81,3
Another point to be discussed at this stage is performance of the model according to type I
and type II error. Table 3 shows performance of the model considering both types of the
errors. The results are given in the fourth column, (a), which is the detection of actual
manipulators and (b), which is the detection of actual nonmanipulator can be adjusted by
setting different t and q values in step I formula presented in section 4.4. Increasing t value
increases (a), and increasing q value increases (b). Several runs during execution of this study,
however, show that (a) value increases as the value of t until it’s value is increased to 3. After
this value (a) doesn’t change even if t value is increased.
Table 3 - Type I and Type II errors of the model.
Calculated M
Calculated NM
Actual
139
32 (type I error)
Manipulators
Actual
Nonmanipulators 375 (type II error) 687
%
0,8129 (a)
Total %
0,66991
0,6469 (b)
At this point, comperative efficiency of the models is another point to be discussed. Another
study which was carried by Küçüksözen and Küçükkocaoğlu (2005) used nearly the same
data in order to detect falsified financial statements by using statistical techniques. In this
study, financial data of 126 Turkish manufacturing companies listed during the period from
1992 through 2002 is processed by using a revised version of Beneish’s (1999) statistical
technique. We have compared the performance of our model with Küçüksözen and
Küçükkocaoğlu’s (2005) application of Beneish Model (1999) and listed the results in Table
4.
22/28
Table 4 - Comperative efficiency of the proposed algorithm and Küçüksözen and
Küçükkocaoğlu’s (2005) application of Beneish Model (1999)
Models
Manipulator Non-Manipulator
Percentage Küçüksözen and Küçükkocaoğlu’s
38%
61%
of Fair
(2005) application of Beneish Model
Prediction (1999)
Cutting Plane Algorithm (CPA)
81%
65%
As seen in Table 4, cutting plane algorithm is much more efficient for detection of
manipulator firms when compared with the Beneish model, i.e %38 for Beneish model and
%81 for cutting plane algorithm. Although performance gap between the models is high for
manipulator firms, it is not so different for nonmanipulator firms, i.e. %61 for Beneish model
and %65 for cutting plane algorithm. As a result, Cutting Plane Algorithm can be said to have
higher performance when compared to Beneish Model.
Conclusion
Turkey, one of the most important and fastest growing economies in the world in recent years,
occupies a central position as the financial and business hub of Middle East region. Besides
being the preferred choice of Multinational Companies direct investment arena, it is also
becoming one of the leading financial markets especially for the Arabic capital investment
funds that was fled from European countries and USA. In order to maintain and enhance the
growing reputation of its financial market, it is important that Turkey continues to adopt
measures that maintain the confidence of international investors. This would include, among
other things, maintaining a high standard of financial reporting.
The main contribution of this paper to the literature is the development and application of a
conceptually new method intended to estimate the approximate amount of earnings
management from the publicly available information. The methodology is based on cutting
plane formulation using mathematical programming where the model improves the major
drawbacks of the existing models and advances the estimation methodologies of earnings
management literature into a new level.
The model deduced from the data of 1997 is used to detect the falsified financial statements
during the years of 1992-2002. As an initial part of the analysis, 1997 data is used to
formulate the model. The results obtained by applying the model and the actual data are
compared in order to calculate the performance of the model introduced.
During the analysis, 10 ratios and indexes are used for detecting falsified financial statements.
One of which out of 10, “financial expenses index”, although not widely used in the earnings
manipulation literature, is included in the model, since it is the most common type of
manipulation example in Turkey.
The model exposed some conclusions about the variables’ effect on the earnings management
potential of the firm, for example, as the gross margin index, sales growth index and leverage
index increases and the probability of manipulation decreases.
23/28
The results of the model show high performance when compared with other statistical
methods used in the earnings management literature. Model’s performance on forecasting the
manipulator firms is 81%, which is a higher value than that of nonmanipulator firms, 65%
numerically. The model introduced also has the flexibility of adjusting the preference of
detecting manipulators over nonmanipulators or vice versa.
When compared with Küçüksözen and Küçükkocaoğlu’s (2005) study which uses probit
technique, using the same data, the three stage algorithm introduced in this paper has 43%
higher detection ability for manipulator cases and 4% higher detection ability for
nonmanipulator cases.
However, given the flexibility of international accounting standards, and the motivations of
managers for misrepresentation, such standards will keep providing opportunities to disclose
false financial statements to the managers. The ability to identify earnings management
practices from the accounting ratios and/or indexes of a particular firm will remain the
privilege of auditors and regulators of tomorrow (Babalyan, 2004).
24/28
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